Multi-Pair Two-Way Massive MIMO Relaying With Zero Forcing: Energy Efficiency and Power Scaling Laws

In this paper, we study a multi-pair two-way half-duplex decode-and-forward (DF) massive multiple-input multiple-output (MIMO) relaying system, in which multiple single-antenna user pairs can exchange information through a massive MIMO relay. For low-complexity processing, zero-forcing reception/zero-forcing transmission (ZFR/ZFT) is employed at the relay. First, we analytically study the large-scale approximations of the sum spectral efficiency (SE). Furthermore, we focus on three specific power scaling laws to study the trade-off between the transmit powers of each pilot symbol, each user and the relay, and also focus on how the transmit powers scale with the number of relay antennas, <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>, to maintain a finite SE performance. Additionally, we consider a practical power consumption model to investigate the energy efficiency (EE), and illustrate the impact of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and the interplay between the power scaling laws and the EE performance. Finally, we consider the system fairness via maximizing the minimum achievable SE among all user pairs.